Abstract : The ground-based Cherenkov telescope array H.E.S.S. High Energy Stereoscopic System is able to detect gamma rays at very high energies E> 50GeV to probe the most violent non-thermal phenomena in the universe. These gamma rays can also come from dark matter particle annihilation. Gamma-ray astronomy provides a promising avenue to search for signatures of these annihilations in overdense regions of the universe. This thesis is composed of three parts. After a brief reminder of the H.E.S.S. instrument, the performance tests to calibrate the new electronics used for the modernization of the four cameras CT1-4 telescopes are presented. The analysis of the upgraded camera raw data shows a reduction global array dead time allowing to maximize the benefit of the stereoscopy between the 5 telescopes. The second part of the thesis deals with 10 years of observations of the Galactic Center region with H.E.S.S. and recent observations taken with the 28-meter-diameter telescope CT5 located at the center of the array. The data analysis towards the central source HESS J1745-290 provides access to events at lower energies 100 GeV. The spectrum of the central source is in very good agreement with the one of HESS J1745-290 measured with CT1-4 and data below 150 GeV enable to connect it to the Fermi 3FGHL J1745.6-2859c source spectrum. In the third part, the 10 years of data in the region of the Galactic Centre with the first phase of H.E.S.S. are scanned for a dark matter annihilation signal using a likelihood method using the spectral and spatial characteristics of the dark matter signal compared to background. No dark matter signal is detected. The constraints are calculated on the annihilation cross section and, for the first time, a ground-based Cherenkov telescope array is capable to probe the thermal cross section in the case of a cuspy dark matter profile. The sensitivity of the annihilation cross section of the H.E.S.S. instrument using CT5 is then presented toward the Galactic Center and the recently discovered dwarf galaxy Reticulum II. The last part of the thesis studies the potential of the future ground-based instrument CTA Cherenkov Telescope Array for the detection of dark matter annihilation signal. Towards the Galactic Center region, the expected dark matter signal is significantly increased by the contribution of gamma rays produced by inverse Compton process of energetic electrons and positrons on ambient radiation fields. The sensitivity obtained enables CTA to probe the thermal cross section in all annihilation channels for a cuspy dark matter profile. The impact on CTA sensitivity of systematic errors and diffuse emission measured by Fermi is also shown. In the case of dwarf galaxy satellites of the Milky Way, the CTA performances enable to consider them as extended objects and provide a competitive sensitivity with the Galactic Centre sensitivity for a kpc-core profile. In the case of a line signal, CTA will be able to strongly constrain specific TeV dark matter models through the Sommerfeld effect, as Wino and MDM-5plet.